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Theorem fsync-pages

cache_fsync-pages#(INODE, DIRS; ERR, FILES, PCACHE, ASYNCED) {ERR := ESUCCESS; let N = 0, INO = INODE.ino, HIT = ?, DIRTY = ? in while N * VFS_PAGE_SIZE < INODE.size ∧ ERR = ESUCCESS do {/* (fsync-pages-overwrite : invariant afs-cons(DIRS, FILES) ∧ pcache-cons(PCACHE, DIRS, FILES) ∧ getinode(INO, DIRS, FILES) = getinode(INO, DIRS, FILES`) ∧ INO = INODE.ino ∧ INO ∈ FILES ∧ (∀ KEY. (KEY ∈ PCACHE ↔ KEY ∈ PCACHE`) ∧ PCACHE[KEY].page = (PCACHE`)[KEY].page ∧ (PCACHE[KEY].dirty → (PCACHE`)[KEY].dirty)) ∧ ( ERR = ESUCCESS → (∀ PAGENO. (PAGENO < N ⊃ (PAGENO ∈ FILES[INO].content ↔ PAGENO ∈ (FILES` ⊕ PCACHE`)[INO].content) ∧ FILES[INO].content[PAGENO] = (FILES` ⊕ PCACHE`)[INO].content[PAGENO] ; (PAGENO ∈ FILES[INO].content ↔ PAGENO ∈ (FILES`)[INO].content) ∧ FILES[INO].content[PAGENO] = (FILES`)[INO].content[PAGENO] )))) */; pcache_check_page#(INO, N, PCACHE; HIT, DIRTY, ERR); if HIT ∧ DIRTY then let PBUF = ? in {pcache_get#(INO, N, PCACHE; HIT, PBUF, ERR); if ERR = ESUCCESS then afs_writepage#(INODE, N, PBUF, DIRS; ERR, FILES; ASYNCED); if ERR = ESUCCESS then afs_check_commit#(DIRS, FILES; ERR; ASYNCED); if ERR = ESUCCESS then {DIRTY := false; pcache_set_status#(INO, N, DIRTY; ERR, PCACHE)}}; N := N + 1} }